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Analytical Studies of Nonlinear Problems in Gravitational Field Theory

Research Project

Project/Area Number 62540279
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 物理学一般
Research InstitutionNagoya University

Principal Investigator

TOMIMATSU Akira  Faculty of Science, Nagoya University, 理学部, 教授 (10034612)

Co-Investigator(Kenkyū-buntansha) NOZAKI Kazuhiro  Faculty of Science, Nagoya University, 理学部, 助教授 (00115619)
TANIUTI Tosiya  Faculty of Science, Nagoya University, 理学部, 教授 (40022503)
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1987: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsNonintegrable System / Gravitational Field Equation / Nonlinear Wave / Reductive Perturbation Method / Perturbation on Soliton / Singular Manifold Expansion / ブラックホール / アインシュタイン方程式 / 非線形重力波 / 非可積分系と近似法 / ソリトン
Research Abstract

This research project aimed to develop analytical methods in nonlinear mathematical physics and to apply them to nonlinear equations in gravitational field theory. The following results were obtained: 1.Developments of analytical methods.(1)By applying the reductive perturbation method to multi-dimensional wave propagation,it was shown that some nonlinear evolutional equations can be reduced to the Kadomtsev-Petviashvili aquation and the Zabolotskaya-Khokhlov equation.(2)Effects of nonintegrable perturbations on soliton systems were studied. It was found that a new stationary nonlinear wave which is different from the soliton can be excited by a weak external force,and a bound 2-soliton can split into individual solitons through a dispersive (or dissipative) perturbation.(3)Some nonintegrable equations were transformed into Hirota's bilinear form by a truncation of the singular manifold expansion,and the explicit solutions were derived.
2.Applications to gravitational field equations.(1)By applying the method of characteristics,a propagation character of nonlinear waves in a string-induced gravity theory was studied. The new black-hole solution which has a thermodynamic property different from the Schwarzschild solution was also derived.(2)By using soliton solutions of the cylindlical Einstein equations,it was shown that the gravitational Faraday rotation due to a nonlinear interaction of gravitational waves occurs effectively. (3)Based on the perturbation theory for the Schwarzschild solution,the ploblem of a head-on collision of two black holes was studied. The initial data were constructed,and the subsequent time-evolution of gravitational field was calculated.The emission of pulse-like waves and the increase increase of the area of black holes were explicitly shown. Further developments of analytical methods in nonintegrable gravitational field equations remain to future investigations.

Report

(3 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • Research Products

    (33 results)

All Other

All Publications (33 results)

  • [Publications] A.Tomimatsu: Prog.Theor.Phys.77. 1014-1018 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A.Tomimatsu: J.Math.Phys.28. 2720-2725 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A.Tomimatsu: Prog.Theor.Phys.79. 86-95 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A.Tomimatsu: Gen.Rel.Grav.21. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A.Tomimatsu: Gen.Rel.Grav.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] T.Taniuti: J.Phys.Soc.Japan. 56. 1286-1288 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] H.Moriguchi: J.Phys.Soc.Japan. 57. 470-475 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] K.Nozaki: J.Phys.Soc.Japan. 56. 3052-3054 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Y.Kodama,: Optics Letters. 12. 1038-1040 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] T.Yamada: J.Phys.Soc.Japan.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] T.Taniuti: "Contributions to Nonlinear Wave Motion,標題:Reductive Perturbation Method for Quasi One-Dimensional Nonlinear Wave Propagation" Longman/Pitman, (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A. Tomimatsu: "Nonlinear Wave Propagation in Gravity Theory with the General Lovelock Lagrangian" Prog. Theor. Phys.77. 1041-1018 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A. Tomimatsu: "Nonlinear Wave Propagation in the Gauss-Bonnet Extended Einstein Theory" J. Math. Phys.28. 2720-2725 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A. Tomimatsu: "Scalar-Coupled Black Holes in Classical Kaluza-Klein Theory with the Lovelock Lagrangian" Prog. Thero. Phys.79. 86-95 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A. Tomimatsu: "The Gravitational Faraday Rotation for Cylindrical Gravitational Solitons" Gen. Rel. Grav.21. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A. Tomimatsu: "Gravitational Field in a collision of Two Schwarzschild Black Holes" Submitted to Gen. Rel. Grav.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] T. Taniuti: "Nonlinear Responses of Dispersive Media" J. Phys. Soc. Japan. 56. 1286-1288 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] H. Moriguchi: "Nonlinear Responses of Dispersive Media II" J. Phys. Soc. Japan. 57. 470-475 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] K. Nozaki: "Hirota's Method and the Singular Manifold Expansion" J. Phys. Soc. Japan. 56. 3052-3054 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Y. Kodama: "Soliton Interaction in Optical Fibers" Optics Letters. 12. 1038-1040 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] T. Yamada: "Effects of Dissipative Perturbation on Bound-State Solitons of Nonlinear Schrodinger Equation" Submitted to J. Phys. Soc. Japan.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] T. Taniuti: Reductive Perturbation Method for Quasi One-Dimensional Nonlinear Wave Propagation; in Contributions to Nonlinear Wave Motion. Longman/Pitman, London, Boston and Melbourne, (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] A.Tomimatsu: Gen.Rel.Grav.21. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] A.Tomimatsu: Gen.Rel.Grav.

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Yamada: J.Phys.Soc.Japan.

    • Related Report
      1988 Annual Research Report
  • [Publications] A. Tomimatsu: Prog. Theor. Phys.77. 1014-1018 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] A. Tomimatsu: J. Math. Phys.28. 2720-2725 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] A. Tomimatsu: Prog. Theor. Phys.79. 86-95 (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] T. Taniuti: J. Phys. Soc. Japan. 56. 1286-1288 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] H. Moriguchi: J. Phys. Soc. Japan. 57. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] K. Nozaki: J. Phys. Soc. Japan. 56. 3052-3054 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Y. Kodama: Optics Letters. 12. 1038-1040 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] T. Taniuti: "Contributions to Nonlinear Wave Motion(edited by J. Engelbrecht) 中,標題;Reductive Perturbation Method for Quasi One Dimensional Nonlinear Wave Propagation" Longman/Pitaman;London;Boston and Melbourne,

    • Related Report
      1987 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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